Abstract

We designed disk patch resonators to meet the requirements for enhanced coupling of optical cavities to intersubband transitions in heterostructures in the terahertz frequency regime. We applied modifications to the standard patch resonator in the form of a chain of holes and slits to control the resonator eigenmodes featuring quality factors ωFWHM/ω0 as high as 40. Due to the broken rotational symmetry of the resonators the individual eigenmodes can be accessed selectively depending on the incidence and the polarization of the THz wave. The demonstrated post-process blue-shifting of the resonance frequency up to 50% is a key tuning knob for an optimization of light-matter interaction in a quantum system.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2016 (1)

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

2014 (6)

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

S. De Liberato, “Light-matter decoupling in the deep strong coupling regime: The breakdown of the purcell effect,” Phys. Rev. Lett. 112, 016401 (2014).
[Crossref] [PubMed]

F. Minkowski, F. Wang, A. Chakrabarty, and Q.-H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104, 021111 (2014).
[Crossref]

P. Jung, A. V. Ustinov, and S. M. Anlage, “Progress in superconducting metamaterials,” Supercond. Sci. Technol. 27, 073001 (2014).
[Crossref]

Yu. Nanfang and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials 13, 139–150 (2014).
[Crossref]

B. Paulillo, J. M. Manceau, A. Degiron, N. Zerounian, G. Beaudoin, I. Sagnes, and R. Colombelli, “Circuit-tunable sub-wavelength THz resonators: hybridizing optical cavities and loop antennas,” Opt. express 22, 21302–21312 (2014).
[Crossref] [PubMed]

2013 (3)

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

D. Dietze, A. Andrews, P. Klang, G. Strasser, K. Unterrainer, and J. Darmo, “Ultrastrong coupling of intersubband plasmons and terahertz metamaterials,” Appl. Phys. Lett. 103, 201106 (2013).
[Crossref]

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

2012 (3)

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nature Materials 11, 917–924 (2012).
[Crossref] [PubMed]

2011 (2)

Yu. Nanfang, P. Gevenet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 334–337 (2011).

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible switching of ultrastrong light-molecule coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

2010 (7)

T. Niemczyk, F. Deppe, H. Huebl, E. Menzel, F. Hocke, M. Schwarz, J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
[Crossref]

N. I. Zheludev, “The road ahead for metamaterials,” Science 328, 582–583 (2010).
[Crossref] [PubMed]

S. M. Anlage, “The physics and applications of superconducting metamaterials,” J. Opt. 13, 024001 (2010).
[Crossref]

S. Zhang, Y.-S. Park, Y. Liu, T. Zentgraf, and X. Zhang, “Far-field measurement of ultra-small plasmonic mode volume,” Opt. Express 18, 6048–6055 (2010).
[Crossref] [PubMed]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the thz frequency range,” Opt. Express 18, 13886–13907 (2010).
[Crossref] [PubMed]

2009 (1)

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

2006 (2)

H. Walther, B. T. Varcoe, B.-G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325 (2006).
[Crossref]

G. Khitrova, H. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[Crossref]

2005 (2)

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
[Crossref]

1999 (1)

J. B. Pendry, A. J. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99 (1954).
[Crossref]

Aieta, F.

Yu. Nanfang, P. Gevenet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 334–337 (2011).

Allerman, A.

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

Anappara, A. A.

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

Andrews, A.

D. Dietze, A. Andrews, P. Klang, G. Strasser, K. Unterrainer, and J. Darmo, “Ultrastrong coupling of intersubband plasmons and terahertz metamaterials,” Appl. Phys. Lett. 103, 201106 (2013).
[Crossref]

Andrews, A. M.

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the thz frequency range,” Opt. Express 18, 13886–13907 (2010).
[Crossref] [PubMed]

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
[Crossref]

Anlage, S. M.

P. Jung, A. V. Ustinov, and S. M. Anlage, “Progress in superconducting metamaterials,” Supercond. Sci. Technol. 27, 073001 (2014).
[Crossref]

S. M. Anlage, “The physics and applications of superconducting metamaterials,” J. Opt. 13, 024001 (2010).
[Crossref]

Bastard, G.

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

Baust, A.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

Beaudoin, G.

B. Paulillo, J. M. Manceau, A. Degiron, N. Zerounian, G. Beaudoin, I. Sagnes, and R. Colombelli, “Circuit-tunable sub-wavelength THz resonators: hybridizing optical cavities and loop antennas,” Opt. express 22, 21302–21312 (2014).
[Crossref] [PubMed]

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

Beck, M.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Becker, T.

H. Walther, B. T. Varcoe, B.-G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325 (2006).
[Crossref]

Beltram, F.

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

Benz, A.

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
[Crossref]

Biasiol, G.

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

Brekenfeld, M.

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Brener, I.

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

Campione, S.

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

Capasso, F.

Yu. Nanfang and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials 13, 139–150 (2014).
[Crossref]

Yu. Nanfang, P. Gevenet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 334–337 (2011).

Capolino, F.

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

Carusotto, I.

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

Castellano, F.

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Cavalié, P.

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

Chakrabarty, A.

F. Minkowski, F. Wang, A. Chakrabarty, and Q.-H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104, 021111 (2014).
[Crossref]

Charpentier, C.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Cibella, S.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Ciuti, C.

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

Colombelli, R.

B. Paulillo, J. M. Manceau, A. Degiron, N. Zerounian, G. Beaudoin, I. Sagnes, and R. Colombelli, “Circuit-tunable sub-wavelength THz resonators: hybridizing optical cavities and loop antennas,” Opt. express 22, 21302–21312 (2014).
[Crossref] [PubMed]

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

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E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
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E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
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Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
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M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108, 106402 (2012).
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T. Niemczyk, F. Deppe, H. Huebl, E. Menzel, F. Hocke, M. Schwarz, J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
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C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
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A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
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G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
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T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible switching of ultrastrong light-molecule coupling,” Phys. Rev. Lett. 106, 196405 (2011).
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T. Niemczyk, F. Deppe, H. Huebl, E. Menzel, F. Hocke, M. Schwarz, J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
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A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
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[Crossref]

Sirtori, C.

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the thz frequency range,” Opt. Express 18, 13886–13907 (2010).
[Crossref] [PubMed]

Solano, E.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

T. Niemczyk, F. Deppe, H. Huebl, E. Menzel, F. Hocke, M. Schwarz, J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Sorba, L.

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

Stewart, W.

J. B. Pendry, A. J. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Strasser, G.

D. Dietze, A. Andrews, P. Klang, G. Strasser, K. Unterrainer, and J. Darmo, “Ultrastrong coupling of intersubband plasmons and terahertz metamaterials,” Appl. Phys. Lett. 103, 201106 (2013).
[Crossref]

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the thz frequency range,” Opt. Express 18, 13886–13907 (2010).
[Crossref] [PubMed]

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
[Crossref]

Strupiechonski, E.

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Teissier, J.

Tetienne, J.-P.

Yu. Nanfang, P. Gevenet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 334–337 (2011).

Tignon, J.

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

Todorov, Y.

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

Y. Todorov, L. Tosetto, J. Teissier, A. M. Andrews, P. Klang, R. Colombelli, I. Sagnes, G. Strasser, and C. Sirtori, “Optical properties of metal-dielectric-metal microcavities in the thz frequency range,” Opt. Express 18, 13886–13907 (2010).
[Crossref] [PubMed]

Tosetto, L.

Tredicucci, A.

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

Unterrainer, K.

D. Dietze, A. Andrews, P. Klang, G. Strasser, K. Unterrainer, and J. Darmo, “Ultrastrong coupling of intersubband plasmons and terahertz metamaterials,” Appl. Phys. Lett. 103, 201106 (2013).
[Crossref]

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
[Crossref]

Ustinov, A. V.

P. Jung, A. V. Ustinov, and S. M. Anlage, “Progress in superconducting metamaterials,” Supercond. Sci. Technol. 27, 073001 (2014).
[Crossref]

Valmorra, F.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Varcoe, B. T.

H. Walther, B. T. Varcoe, B.-G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325 (2006).
[Crossref]

Walther, H.

H. Walther, B. T. Varcoe, B.-G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325 (2006).
[Crossref]

Wang, F.

F. Minkowski, F. Wang, A. Chakrabarty, and Q.-H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104, 021111 (2014).
[Crossref]

Wegscheider, W.

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

Wei, Q.-H.

F. Minkowski, F. Wang, A. Chakrabarty, and Q.-H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104, 021111 (2014).
[Crossref]

Wendt, J.

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

Wulschner, F.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

Xie, E.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

Xu, G.

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

Zentgraf, T.

Zerounian, N.

Zhang, S.

Zhang, X.

Zheludev, N. I.

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nature Materials 11, 917–924 (2012).
[Crossref] [PubMed]

N. I. Zheludev, “The road ahead for metamaterials,” Science 328, 582–583 (2010).
[Crossref] [PubMed]

Zhong, L.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

Zobl, R.

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
[Crossref]

Zueco, D.

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

T. Niemczyk, F. Deppe, H. Huebl, E. Menzel, F. Hocke, M. Schwarz, J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Appl. Phys. B (1)

E. Strupiechonski, G. Xu, P. Cavalié, N. Isac, S. Dhillon, J. Tignon, G. Beaudoin, I. Sagnes, A. Degiron, and R. Colombelli, “Hybrid electronic-photonic subwavelength cavities operating at terahertz frequencies,” Appl. Phys. B 87, 041408 (2013).

Appl. Phys. Lett. (3)

D. Dietze, A. Andrews, P. Klang, G. Strasser, K. Unterrainer, and J. Darmo, “Ultrastrong coupling of intersubband plasmons and terahertz metamaterials,” Appl. Phys. Lett. 103, 201106 (2013).
[Crossref]

F. Minkowski, F. Wang, A. Chakrabarty, and Q.-H. Wei, “Resonant cavity modes of circular plasmonic patch nanoantennas,” Appl. Phys. Lett. 104, 021111 (2014).
[Crossref]

G. Fasching, A. Benz, K. Unterrainer, R. Zobl, A. M. Andrews, T. Roch, W. Schrenk, and G. Strasser, “Terahertz microcavity quantum-cascade lasers,” Appl. Phys. Lett. 87, 1112 (2005).
[Crossref]

Applied Physics Letters (1)

E. Strupiechonski, G. Xu, M. Brekenfeld, Y. Todorov, N. Isac, A. M. Andrews, P. Klang, C. Sirtori, G. Strasser, A. Degiron, and R. Colombelli, “Sub-diffraction-limit semiconductor resonators operating on the fundamental magnetic resonance,” Applied Physics Letters 100, 131113 (2012).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

J. Opt. (1)

S. M. Anlage, “The physics and applications of superconducting metamaterials,” J. Opt. 13, 024001 (2010).
[Crossref]

Nano Lett. (1)

M. Kuttge, F. J. García de Abajo, and A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10, 1537–1541 (2010).
[Crossref]

Nature Comm. (1)

A. Benz, S. Campione, S. Liu, I. Montano, J. Klem, A. Allerman, J. Wendt, M. Sinclair, F. Capolino, and I. Brener, “Strong coupling in the sub-wavelength limit using metamaterial nanocavities,” Nature Comm. 4, 2882 (2013).
[Crossref]

Nature Materials (2)

N. I. Zheludev and Y. S. Kivshar, “From metamaterials to metadevices,” Nature Materials 11, 917–924 (2012).
[Crossref] [PubMed]

Yu. Nanfang and F. Capasso, “Flat optics with designer metasurfaces,” Nature Materials 13, 139–150 (2014).
[Crossref]

Nature Phys. (1)

T. Niemczyk, F. Deppe, H. Huebl, E. Menzel, F. Hocke, M. Schwarz, J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, “Circuit quantum electrodynamics in the ultrastrong-coupling regime,” Nature Phys. 6, 772–776 (2010).
[Crossref]

Nature Physics (1)

G. Khitrova, H. Gibbs, M. Kira, S. W. Koch, and A. Scherer, “Vacuum rabi splitting in semiconductors,” Nature Physics 2, 81–90 (2006).
[Crossref]

Opt. Express (2)

Phys. Rev. (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93, 99 (1954).
[Crossref]

Phys. Rev. B (3)

C. Maissen, G. Scalari, F. Valmorra, M. Beck, J. Faist, S. Cibella, R. Leoni, C. Reichl, C. Charpentier, and W. Wegscheider, “Ultrastrong coupling in the near field of complementary split-ring resonators,” Phys. Rev. B 90, 205309 (2014).
[Crossref]

C. Ciuti, G. Bastard, and I. Carusotto, “Quantum vacuum properties of the intersubband cavity polariton field,” Phys. Rev. B 72, 115303 (2005).
[Crossref]

A. A. Anappara, S. De Liberato, A. Tredicucci, C. Ciuti, G. Biasiol, L. Sorba, and F. Beltram, “Signatures of the ultrastrong light-matter coupling regime,” Phys. Rev. B 79, 201303 (2009).
[Crossref]

Phys. Rev. Lett. (4)

T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Reversible switching of ultrastrong light-molecule coupling,” Phys. Rev. Lett. 106, 196405 (2011).
[Crossref] [PubMed]

S. De Liberato, “Light-matter decoupling in the deep strong coupling regime: The breakdown of the purcell effect,” Phys. Rev. Lett. 112, 016401 (2014).
[Crossref] [PubMed]

M. Geiser, F. Castellano, G. Scalari, M. Beck, L. Nevou, and J. Faist, “Ultrastrong coupling regime and plasmon polaritons in parabolic semiconductor quantum wells,” Phys. Rev. Lett. 108, 106402 (2012).
[Crossref] [PubMed]

Y. Todorov, A. M. Andrews, R. Colombelli, S. De Liberato, C. Ciuti, P. Klang, G. Strasser, and C. Sirtori, “Ultrastrong light-matter coupling regime with polariton dots,” Phys. Rev. Lett. 105, 196402 (2010).
[Crossref]

Physical Review B (1)

A. Baust, E. Hoffmann, M. Haeberlein, M. J. Schwarz, P. Eder, J. Goetz, F. Wulschner, E. Xie, L. Zhong, F. Quijandría, D. Zueco, J.-J. G. Ripoll, L. García-Álvarez, G. Romero, E. Solano, K. G. Fedorov, E. P. Menzel, F. Deppe, A. Marx, and R. Gross, “Ultrastrong coupling in two-resonator circuit qed,” Physical Review B 93, 214501 (2016).
[Crossref]

Rep. Prog. Phys. (1)

H. Walther, B. T. Varcoe, B.-G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys. 69, 1325 (2006).
[Crossref]

Science (2)

N. I. Zheludev, “The road ahead for metamaterials,” Science 328, 582–583 (2010).
[Crossref] [PubMed]

Yu. Nanfang, P. Gevenet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 334–337 (2011).

Supercond. Sci. Technol. (1)

P. Jung, A. V. Ustinov, and S. M. Anlage, “Progress in superconducting metamaterials,” Supercond. Sci. Technol. 27, 073001 (2014).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

(a) Sketch of a standard split ring (LC) resonator and its lumped elements model; (b) Sketch of a modified disk path resonator and its lumped elements model; (c,d) Cross-section and top view of the resonator showings a LC resonator consisting of two capacitors C1 and C2 connected via top and bottom conductor forming a loop with inductance L; (e) Frequency of the LC resonant mode of disk patch resonator as a function of geometrical parameters of the conductor obtained by 2D eigenmode simulation (colored symbols) and from the LC model (black solid lines).

Fig. 2
Fig. 2

Electric field distribution of the eigenmodes up to 3.2 THz of (a) the disk patch resonator (DP), (b) the split disk patch resonator (SDP) and (c) the double split disk patch resonator (dSDP) with a radius of 21 µm and a dielectric layer (GaAs) thickness of 4 µm. The eigenfrequencies of individual modes are listed in Table 1. The mode notation e/omn reflects orders of angular m and radial n modes according to Ref. [26]. Subscript ρ is assigned to modes derived from the axisymmetric mode e02; axis related subscripts refer to orientation of the axis of symmetry for the mode pattern.

Fig. 3
Fig. 3

Tuning the split disk resonator by partially removing the dielectrics. 3D schematic sketch of (a) the initial unetched case; (b) the intermediate state after anisotropic etching of the dielectric and (c) the final state (removed top electrode on one side is for the sake of clarity to emphasise the top electrode undercut). (d) and (e) Electric displacement field Dz and the magnitude of magnetic field |B| of the axisymmetric eigenmodes e02 for the initial unetched case and the final case, respectively.

Fig. 4
Fig. 4

(left) Tuning of the resonance frequency for etching the dielectric anisotropically down to the ground layer and subsequently for etching isotropically underneath the top layer. (right) Electric and the magnetic field distribution for various etch steps.

Fig. 5
Fig. 5

SEM micrograph of (a) a SDP resonator, and (b) a dSDP resonator. The THz light pulses are incident at 45° with p-polarization. Each structure is measured for two different orientations as indicated in the images.

Fig. 6
Fig. 6

Comparison of the measured SDP reflectance spectra (top row) with 3D simulations (bottom row). In the experiment the resonators were excited at 45° incidence in (a) with the electric field parallel to the slit (Ex), and (b) orthogonal to the slit (Ey), see Fig. 5(a). The spectra were measured for the initial unetched case and after stepwise anisotropic (aniso) or isotropic (iso) dry etching. (c), (d) In the 3D simulations the resonators are excited for the same angle of incidence and the same configuration of the dielectric environment as in the experiment.

Fig. 7
Fig. 7

Comparison of the measured dSDP reflectance spectra (top row) with 3D simulations (bottom row). In the experiment the resonators were excited at 45° incidence in (a) with the electric field orthogonal the one of slits (Ey), and (b) at azimuthal angle of 45° to slits (Exy), see Fig. 5(b). The reflectance spectra were measured for the initial unetched case and after two etch steps of anisotropic etching (aniso). (c), (d) In the 3D simulations the resonators are excited for the same angle of incidence and the same configuration of the dielectric environment as in the experiment.

Fig. 8
Fig. 8

The eigenfrequencies (a,b) and the Q factors (c,d) of the SDP and dSDP resonator as a function of the etching depth in the dielectric extracted from the measured reflectance spectra in Figs. 6(a,b) and Figs. 7(a,b). The color of symbols assigned to the individual eigenmode indicates the orientation of incident electric field (red - Ex, blue - Ey, green -45°/Exy).

Tables (1)

Tables Icon

Table 1 Summary of the eigenfrequencies in THz of the modes shown in Fig. 2. We utilize the mode notation from [26]. The additional letters and the prime denote modes that are generated by breaking the symmetry. y and xy describe the orientation of the modes and the relation to the incidence Ex and Exy of the light that can excite those modes. ρ states the relation to the axisymmetric mode e02.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

ν 1 2 π L C 1 h loop ln ( r disk + w loop r i , loop ) w loop r i , loop 1 h loop w loop r i , loop .

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